This study deals with the effects of branching in some high polymers on viscosity behaviour and on the rela­tionship between intrinsic viscosity and molecular weight. First, the preparation of branched polymers by means of graft polymerization is described. Evidence for the occurrence of grafting, which would result in the growth of polystyrene branches on a min, or backbone, chain com­posed of polystyrene or a copolymer of styrene and li-vinyl-cyclohexene-1, is reviewed, Next, the design, construction, and calibration of a flexible light scattering photometer is described. The performance of this instrument is shown to bs adequate for the determination of the molecular weight and size, as well as the second virial coefficient, of a high polymer in solu­tion. Finally, properties of the graft polymers in solu­tion are compared, with the corresponding properties of linear polystyrene. The relationships found between intrin­sic viscosity and molecular weight, as well as the values obtained for the second virial coefficient, confirm the ex­istence of branching in the graft polymers. On the other hand, it is shown that the viscosity slope constant, Huggins' k', the of which, is often used as an indication of branching, is not affected significantly by the branching present in the graft polymers. / Thesis / Doctor of Philosophy (PhD)

This work addresses the problem of rendering clouds. The task of rendering clouds is important to film and video game directors who want to use clouds to further the story or create a specific atmosphere for the audience. While there has been significant progress in this area, other solutions to this problem are inadequate because they focus on speed instead of accuracy, or focus only on a few specific properties of rendered clouds while ignoring others. Another common shortcoming with other methods is that they are not integrated into existing rendering pipelines. We propose a solution to this problem based on creating a point cloud to represent the cloud volume, then calculating light scattering events between the points. The key insight is blending isotropic and anisotropic scattering events to mimic realistic light scattering of anisotropic participating media. Rendered images are visually plausible representations of how light interacts with clouds.

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Polarimetry is one of the principal means of investigating the interaction of light with matter. Theoretical models and experimental techniques are presented in this dissertation for polarimetric characterization of random electromagnetic beams and of signatures of random media in different scattering regimes and configurations. The degree of polarization rather than the full description of the state of polarization is of interest in multiple scattering and free space propagation where the statistical nature and not the deterministic component of light bears the relevant information. A new interferometric technique for determining the degree of polarization by measuring the intensity fluctuations in a Mach-Zehnder interferometric setup is developed. For this type of investigations, one also needs a light source with a controllable degree of polarization. Therefore, also based on a Mach-Zehnder interferometer, we proposed a new method for generating complex random electromagnetic beams. As a direct application of the cross-spectral density matrix formalism, it is shown that the spectral and the polarimetric characteristics of light can be controlled by adjusting the correlations between parallel components of polarization propagating through the two arms of the interferometer. When optical beams are superposed in the previous applications it is desirable to understand how their coherence and polarimetric characteristics are combined. A generalization of the interference laws of Fresnel and Arago is introduced and as a direct application, a new imaging polarimeter based on a modified Sagnac interferometer is demonstrated. The system allows full polarimetric description of complex random electromagnetic beams. In applications such as active illumination sensing or imaging through turbid media, one can control the orientation of the incident state of polarization such that, in a given coordinate system, the intensities are equal along orthogonal directions. In this situation, our novel interferometric technique has a significant advantage over standard Stokes imaging polarimetry: one needs only one image to obtain both the degree of polarization and the retardance, as opposed to at least three required in classical Stokes polarimetry. The measurement of the state of polarization is required for analyzing the polarization transfer through systems that alter it. Two innovative Mueller matrix measurement techniques are developed for characterizing scattering media, either in quasi real-time, or by detection of low level signals. As a practical aspect of Mueller polarimetry, a procedure for selecting the input Stokes vectors is proposed. The polarimetric signatures of different particulate systems are related to their structural properties and to the size distribution, shape, orientation, birefringent or dichroic properties of the particles. Various scattering regimes and different geometries are discussed for applications relevant to the biomedical field, material science, and remote sensing. The analysis is intended to elucidate practical aspects of single and multiple scattering on polydisperse systems that were not investigated before. It seems to be generally accepted that depolarization effects can only be associated to multiple scattering. It is demonstrated in this dissertation that depolarization can also be regarded as an indication of polydispersity in single scattering. In order to quantify the polarizing behavior of partially oriented cylinders, the polarization transfer for systems consisting of individual layers of partially aligned fibers with different degrees of alignment and packing fractions is also analyzed in this dissertation. It is demonstrated that a certain degree of alignment has the effect of a partial polarizer and that the efficiency of this polarizer depends on the degree of alignment and on the packing fraction of the system. In specific applications such as long range target identification, it is important to know what type of polarization is better preserved during propagation. The experimental results demonstrate that for spherical particles smaller than the wavelength of light, linear polarization is better preserved than circular polarization when light propagates through turbulent media. For large particles, the situation is reversed; circular polarization is better preserved. It is also demonstrated here that this is not necessarily true for polyhedral or cylindrical particles, which behave differently. Optical activity manifests as either circular birefringence or circular dichroism. In this dissertation, a study is presented where both the effect of optical activity and that of multiple scattering are considered. This situation is relevant for medical applications and remote sensing of biological material. It is demonstrated here that the output state of polarization strongly depends on the optical density of the scattering medium, the optical rotatory power and the amount of circular dichroism associated to the scattering medium. This study shows that in the circular birefringence case, scattering and optical activity work together in depolarizing light, while in the dichroic case the two effects compete with each other and the result is a preservation of the degree of polarization. To characterize highly diffusive media, a very simple model is developed, in which the scattering is analyzed using the Mueller matrix formalism in terms of surface and volume contributions.

The three projects utilized polymer physics theories to investigate polymer aggregation mechanics. Dynamic light scattering (DLS), static light scattering (SLS) and small angle light scattering (SALS) were the primary characterization tools. The goal of the first project was to study the aggregation of bovine βL-crystallin and apply that knowledge towards cataract formation, which is caused by aggregation of the crystallins. The first series of experiments characterized the kinetics of α-crystallin and βL-crystallin in water at room temperature. α-crystallin’s equilibrium hydrodynamic radius value was kinetically independent. βL-crystallin formed an aggregate with an Rh that was kinetically dependent. The packing structure of the aggregate formed by βL-crystallin was determined to be loosely packed using SLS. α -crystallin was uniquely demonstrated to be a chaperone in a way that indicated electrostatics played a significant role in aggregation. The role of electrostatics led to an investigation into sodium chloride. Sodium chloride proved to reduce the βL-crystallin aggregate size. The next series of experiments simulated biological conditions using a phosphate buffered saline (PBS). The experiments were performed at 35oC. α -crystallin and βL-crystallin were shown to be kinetically independent and demonstrate equilibrium Rh values on the time scale that the experiments were performed. A pH study revealed that multiple size-scales were present only at physiological pH. Above and below physiological pH, only two aggregate size-scales existed. A charge model was made of βL-crystallin to compare theory with experimental results. The future goal of project is to reproduce these experiments with human crystallins. In the second project, by changing the order and arrangement of β-spiral elastin (E) and α -helical COMPcc (C) the macroscopic structure was controlled. The EC diblock exhibited a fast and slow mode below the transition temperature of 25oC and single mode behavior above the transition. Phase separation occurred above the transition. CE showed three different size-scales below the transition of 15oC and demonstrated spinodal decomposition above the transition. The ECE triblock demonstrated bimodal behavior below the transition of 25oC and one micellar size above the transition. α-helical COMPcc has the ability to bind to small molecules, making the findings from this project instrumental in creating a drug delivery vehicle. The third project investigated sodium polystyrene sulfonate and polyethylene oxidepolypropylene oxide-polyethylene oxide in solution. Both systems self-assemble into aggregate structures at specific conditions. The significant difference between these two polymers is that sodium polystyrene sulfonate is a polyelectrolyte. It is well known that aggregate structures can be formed by variation in temperature and concentration. However, by having a charged polymer in solution with a neutral polymer the aggregate structure can also be controlled by changing the pH and adding salt to the solution, as was performed in the first project. The third project is an excellent conclusion to the previous two because it allows for the aggregate structure to be controlled even more so than in the previous projects by mediating the polydispersity index, molecular weight and concentration of each component. Each project focused on a different method of mediating the aggregate structure. A better understanding of aggregation has applications in industry and medicine. Polymer physics theory is instrumental in understanding aggregation mechanics.

<p> The models derived from classical light scattering theory for predicting Rayleigh light scattering contain useful parameters such as polymer weight average molecular weight, z-average radius of gyration and virial coefficients. The methods used to estimate these model parameters have not been based on sound statistical principles. It is with improved statistical estimation methods for these parameters that this thesis is concerned with. The methods of linear least squares, non-linear least squares and error propagation were applied to the analysis of wide angle and low angle laser light scattering data and the results compared.</p> <p> From the theory of dynamic light scattering, methods have been developed to reconstruct particle size distributions of unimodal, bimodal and polydisperse polymer solutions from the data accumulated in a single experiment. Some of these methods of reconstruction are based upon the estimation of the coefficients in a sum of exponentials. Estimating sums of exponentials is a highly ill-conditioned problem and the problems encountered thereof are examined in this thesis. Linear least squares, non-linear least squares and exponential sampling techniques were applied to experimental data from a number of simulated polymer distributions and the final results compared.</p> / Thesis / Master of Engineering (MEngr)

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